Abstract
This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.
| Original language | English |
|---|---|
| Pages (from-to) | 485-497 |
| Number of pages | 13 |
| Journal | Insurance: Mathematics and Economics |
| Volume | 40 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 2007 May 1 |
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Keywords
- Circumstance process
- Discounted aggregate claims
- Laplace-Stieltjes transform
- Moments
ASJC Scopus subject areas
- Statistics, Probability and Uncertainty
- Economics and Econometrics
Cite this
Moments of claims in a Markovian environment. / Kim, Bara; Kim, Hwa Sung.
In: Insurance: Mathematics and Economics, Vol. 40, No. 3, 01.05.2007, p. 485-497.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Moments of claims in a Markovian environment
AU - Kim, Bara
AU - Kim, Hwa Sung
PY - 2007/5/1
Y1 - 2007/5/1
N2 - This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.
AB - This paper considers discounted aggregate claims when the claim rates and sizes fluctuate according to the state of the risk business. We provide a system of differential equations for the Laplace-Stieltjes transform of the distribution of discounted aggregate claims under this assumption. Using the differential equations, we present the first two moments of discounted aggregate claims in a Markovian environment. We also derive simple expressions for the moments of discounted aggregate claims when the Markovian environment has two states. Numerical examples are illustrated when the claim sizes are specified.
KW - Circumstance process
KW - Discounted aggregate claims
KW - Laplace-Stieltjes transform
KW - Moments
UR - http://www.scopus.com/inward/record.url?scp=33847302482&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33847302482&partnerID=8YFLogxK
U2 - 10.1016/j.insmatheco.2006.07.004
DO - 10.1016/j.insmatheco.2006.07.004
M3 - Article
AN - SCOPUS:33847302482
VL - 40
SP - 485
EP - 497
JO - Insurance: Mathematics and Economics
JF - Insurance: Mathematics and Economics
SN - 0167-6687
IS - 3
ER -